Kocaeli University / European Credit Transfer System (ECTS)

Name of Lecturer(s)

Associate Prof. Dr. Süleyman EKEN
Research Assistant Seda BALTA

Learning Outcomes of the Course Unit
Program Competencies-Learning Outcomes Relation

Learning Outcomes of the Course Unit

1) Understands the basic principles of propositional and predicate logic.
2) Understands mathematical proof methods and applies them to problem solving
3) Solves some non-continuous problems by modeling them at a basic level with the help of recurrence equations.
4) Explains the concept of complexity in algorithms.
5) Shows relations and determines their properties.
6) Shows functions and determines their properties.
7) Distinguish basic discrete data structures.
8) Formulates counting and discrete random variable probabilities.

Program Competencies-Learning Outcomes Relation

Program Competencies

Learning Outcomes

High

Middle

No relation

Mode of Delivery

Face to Face

Prerequisites and Co-Requisites

None

Recommended Optional Programme Components

Not Required

Course Contents

Küme teorisi, Mantıksal önermeler, Matematiksel ispat yöntemleri Bağıntılar ve fonksiyonlar, Boole cebri ve mantıksal fonksiyonlar Sayı ve kodlama teorisi, Logaritma, olasılık Asimtotik notasyonlar, Toplamlar Kombinatorik teori, temel sayma kuralları, permutasyonlar, kombinasyonlar Üretici fonksiyonlar, basit ve üstel üretken Fonksiyonlar Yineleme (reccurence) bağıntıları ve çözümler, homojen ve homojen olmayan yineleme bağıntıları Graf Teorisi, basit ve yönlü graflar, graflarda bağlılık, Euler ve hamilton grafları Düğüm boyama ve düzlemsel grafler Ağaç yapıları ve uygulamaları, ikili ağaçlar kapsama ağaçları Kapsama Ağacı problemleri Kruskal’s ve greedy algoritması En Kısa yol problemleri Sonlu durumlu makinalar ve Otomata Sonlu durumlu makina, akseptörler ve string tanıma, dönüştürücüler, turing makinalar

Weekly Schedule

1) Propositional logic
2) Predicate logic
3) Sets
4) Matrix, integers, division, prime numbers, modular arithmetic
5) Relations
6) Functions
7) Combinatorics
8) Proofs
9) Midterm exam
10) Graps
11) Trees
12) Discrete Probability
13) Complexity
14) Variable and their types
15) Intro to Automata
16) Final exam

Planned Learning Activities and Teaching Methods

Assessment Methods and Criteria

Contribution of Midterm Examination to Course Grade	50%
Contribution of Final Examination to Course Grade	50%
Total	100%

Language of Instruction

Turkish

Work Placement(s)